# Robo-advising: Learning Investors' Risk Preferences via Portfolio Choices

arXiv: https://arxiv.org/abs/1911.02067 · HTML: https://mlsanity.com/paper/1911.02067/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2019.

## Built on by (most cited first, 7 of 7)

- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [The Evolution of Reinforcement Learning in Quantitative Finance: A Survey](https://mlsanity.com/paper/2408.10932/) (2024)
- [Risk-Aware Linear Bandits: Theory and Applications in Smart Order Routing](https://mlsanity.com/paper/2208.02389/) (2022)
- [Inference of Utilities and Time Preference in Sequential Decision-Making](https://mlsanity.com/paper/2405.15975/) (2024)
- [Hierarchical AI Multi-Agent Fundamental Investing: Evidence from China's A-Share Market](https://mlsanity.com/paper/2510.21147/) (2025)
- [A Noise-Robust Elicit-to-Optimize Framework for Distortion Riskmetrics via Inverse Reinforcement Learning](https://mlsanity.com/paper/2607.14373/) (2026)
- [Uncovering expert objectives in production planning via inverse optimization: An industrial case study](https://mlsanity.com/paper/2608.07398/) (2026)

## Abstract (arXiv)

We introduce a reinforcement learning framework for retail robo-advising. The robo-advisor does not know the investor's risk preference, but learns it over time by observing her portfolio choices in different market environments. We develop an exploration-exploitation algorithm which trades off costly solicitations of portfolio choices by the investor with autonomous trading decisions based on stale estimates of investor's risk aversion. We show that the algorithm's value function converges to the optimal value function of an omniscient robo-advisor over a number of periods that is polynomial in the state and action space. By correcting for the investor's mistakes, the robo-advisor may outperform a stand-alone investor, regardless of the investor's opportunity cost for making portfolio decisions.